Figure 4
Mutual enhancement and formation of multicluster chimera states.
(a) Schematic illustration of m = 3 cluster chimera states in certain range of η. The colors represent the values of the order parameter R and the regions centered with red and blue colors correspond to coherent and incoherent groups of oscillators, respectively. The reference oscillator for calculating the enhancement factor I is the bottom node at the center of the coherent group. (b) Enhancement factor I for the reference oscillator as a function of η, for different values of m. The regions of maximum I values among the different m curves are specified as bold lines, which can be regarded, approximately, as the regions in which the corresponding m-cluster chimera states emerge. (c) Regions of m-cluster chimera states predicted by our mutual-enhancement theory (the colored thick horizontal lines at different m levels), including the main regions m = 4, 3, 5, 7 and 9 and the two subregions with 3&6-cluster and 5&10-cluster chimera states. The white and gray backgrounds have the same meaning as those in Fig. 2, i.e., they denote the regions of m-cluster chimera states, which are obtained from both simulation of Eq. (1) and solution of Eq. (5). The subregions for 3&6-cluster and 5&10-cluster chimera states obtained from Eqs (1) and (5) are also specified with the thin black vertical lines and the corresponding notations.
